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E39 (1997 - 2003) The BMW 5-Series (E39 chassis) was introduced in the United States as a 1997 model year car and lasted until the 2004 when the E60 chassis was released. The United States saw several variations including the 525i, 528i, 530i and 540i. -- View the E39 Wiki

The question is for real. Can the chirp when locking/unlocking the car start to fade? Because I believe mine isn't that loud anymore. I think it's considerably quieter.
Does that horn that is in the right rear wheel well wear out?

Actually, yes, horns do degrade. The horn on my daughter's Civic gave up the ghost. Usually they just fail suddenly but this one got progressively quieter and quieter. And the tone changed. Since this horn has no major functional purpose, I'd ignore the problem. Just look at the car when pressing the key button and the flashing light will tell you it is locking properly.

Actually, yes, horns do degrade. The horn on my daughter's Civic gave up the ghost. Usually they just fail suddenly but this one got progressively quieter and quieter. And the tone changed. Since this horn has no major functional purpose, I'd ignore the problem. Just look at the car when pressing the key button and the flashing light will tell you it is locking properly.

Fudman, that is an accurate description on what happens on my car: it gets progressively quieter. If you lock the car from the passenger side, you can still hear the chirp. If you lock it on the driver side, now you can barely hear it.
Any idea what "degrades"? I read somwhere that the alarm horn has an integrated battery. If so, can this be the cause? And if yes, can one replace that battery? Or you need to buy a new alarm horn?
The reason I want this, a loud alarm is helpful if someone tries to mess with your car.

My hearing isn't what it used to be, but I noticed that sometimes I wouldn't hear the chirp. I also noticed that one of the lock actuators was operating after the others.

I was having an intermittent brake light failure, so I cleaned the grounds in the right rear side. Then I checked the wiring harness that goes through the rubber tube into the trunk. I found a wire on which the insulation was broken. This was the red/black wire that supplies power to the trunk lock through fuse 53. I wrapped some tape around the wire and the whole harness.

I don't know if it was wrapping the wire or cleaning the grounds or something else or just luck, but since then the locking and the chirp and actuators work like normal.